Conditional cumulants in a weakly non-linear regime

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10 Citations (Scopus)


We introduce conditional cumulants as a set of unique statistics closely related to N-point correlation functions and to cumulants of moments of counts in cells. We show that they can be viewed in three equivalent ways: (i) as particular integrals of the N-point correlation functions, (ii) as integrated monopole moments of the bispectrum, and (iii) as statistics associated with neighbour counts. As monopole statistics, they carry similar information to the cumulants S N, the most widely spread higher-order statistics usually measured from counts in cells. While it has been proved that counts in cells can only be approximately corrected for edge effects, we show that well-tested, edge-corrected estimators can be successfully adapted for conditional cumulants. Since edge-effect errors typically dominate large scales, it is expected that it will be possible to measure conditional cumulants with higher accuracy in the interesting large-scale regime. To lay the theoretical ground work for future applications, we compute the predictions of weakly non-linear perturbation theory for conditional cumulants. We demonstrate the use of edge-corrected estimators in a set of simulations and measure conditional cumulants, and compare the results with our theoretical predictions in real and redshift space. We find excellent agreement, especially on scales ≳20 h -1 Mpc. Owing to their advantageous statistical properties and well-understood dynamics, we propose conditional cumulants as tools for high-precision cosmology. Potential applications include constraining bias and redshift distortions from galaxy redshift surveys.

Original languageEnglish
Pages (from-to)357-361
Number of pages5
JournalMonthly Notices of the Royal Astronomical Society
Issue number1
Publication statusPublished - Jul 21 2005


  • Cosmology: theory
  • Large-scale structure of Universe
  • Methods: statistical

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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